John Wells's phonetic blog: what's important in intonation for EFL? | TELT |
Wells quotes Francis Nolan on priorities for learners:

…I will suggest that what learners need is a strategy which will optimise the pedagogical cost-benefit ratio in terms of (in order of priority) intelligibility, the avoidance of inadvertent offence, and (lowest in priority) the mastery of intonational nuances. Broadly corresponding to these three goals would be three prioritised learning targets: the mastery of accentuation (involving stress placement, rhythm, and pitch prominence achieved by a reduced inventory of pitch accents); the eradication of any L1-influenced phonetic realisations of pitch accents which might convey unintended meaning in English; and (lowest in priority) the acquisition of a more complete set of intonational pitch contrasts.